A260854 Base-4 representation of a(n) is the concatenation of the base-4 representations of 1, 2, ..., n, n-1, ..., 1.

0, 1, 25, 441, 27961, 7148857, 1830131001, 468514084153, 119939614479673, 30704541449950521, 7860362613477971257, 2012252829087011018041, 515136724246861226808633, 131875001407205856562222393, 33760000360244849399916500281, 8642560092222683848298425324857

Offset

0,3

Comments

The base 4 is listed in A260343, which means that a(4) = A260851(4) = 27961 is prime and therefore in A260852. See these sequences for more information.

Links

Table of n, a(n) for n=0..15.

D. Broadhurst, Primes from concatenation: results and heuristics, NmbrThry List, August 1, 2015

Example

a(0) = 0 is the result of the empty sum corresponding to 0 digits.
a(2) = 25 = 16 + 2*4 + 1 = 121_4 is the concatenation of (1, 2, 1).
a(4) = 27961 = 12310321_4 is the concatenation of (1, 2, 3, 10, 3, 2, 1), where the middle "10" is the base-4 representation of 4.

Prog

(PARI) a(n, b=4)=sum(i=1, #n=concat(vector(n*2-1, k, digits(min(k, n*2-k), b))), n[i]*b^(#n-i))

Crossrefs

Base-4 variant of A173426 (base 10) and A173427 (base 2). See A260853 - A260866 for variants in other bases b = 3, ..., 16.

Sequence in context: A368161 A264382 A337901 * A001714 A016633 A001811

Adjacent sequences: A260851 A260852 A260853 * A260855 A260856 A260857

Keyword

nonn,base

Author

M. F. Hasler, Aug 01 2015

Status

approved